Displacement for cube
I would suggest baking the high poly mesh to a normal map in Cycles and plugging the generated image into the material for the low poly box using the node editor. There are many great tutorials on this workflow, including: https://youtu.be/BOYRCI-dtjU. It produces consistent results.

You may want to triangulate the low poly mesh first if you are going to export it to a game engine such as Unity, as they may calculate triangles differently.